| 1 | double _pearl_necklace_kernel(double q, double radius, double edge_sep, |
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| 2 | double thick_string, double num_pearls, double sld_pearl, |
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| 3 | double sld_string, double sld_solv); |
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| 4 | double form_volume(double radius, double edge_sep, |
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| 5 | double thick_string, double num_pearls); |
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| 6 | |
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| 7 | double Iq(double q, double radius, double edge_sep, |
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| 8 | double thick_string, double num_pearls, double sld, |
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| 9 | double string_sld, double solvent_sld); |
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| 10 | |
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| 11 | #define INVALID(v) (v.thick_string >= v.radius || v.num_pearls <= 0) |
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| 12 | |
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| 13 | // From Igor library |
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| 14 | double _pearl_necklace_kernel(double q, double radius, double edge_sep, double thick_string, |
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| 15 | double num_pearls, double sld_pearl, double sld_string, double sld_solv) |
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| 16 | { |
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| 17 | //relative slds |
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| 18 | double contrast_pearl = sld_pearl - sld_solv; |
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| 19 | double contrast_string = sld_string - sld_solv; |
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| 20 | |
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| 21 | // number of string segments |
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| 22 | num_pearls = floor(num_pearls + 0.5); //Force integer number of pearls |
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| 23 | double num_strings = num_pearls - 1.0; |
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| 24 | |
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| 25 | // center to center distance between the neighboring pearls |
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| 26 | double A_s = edge_sep + 2.0 * radius; |
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| 27 | |
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| 28 | // Repeated Calculations |
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| 29 | double sincasq = sinc(q*A_s); |
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| 30 | double oneminussinc = 1 - sincasq; |
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| 31 | double q_r = q * radius; |
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| 32 | double q_edge = q * edge_sep; |
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| 33 | |
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| 34 | // each volume |
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| 35 | double string_vol = edge_sep * M_PI * thick_string * thick_string / 4.0; |
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| 36 | double pearl_vol = M_4PI_3 * radius * radius * radius; |
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| 37 | |
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| 38 | //total volume |
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| 39 | double tot_vol; |
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| 40 | //each masses |
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| 41 | double m_r= contrast_string * string_vol; |
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| 42 | double m_s= contrast_pearl * pearl_vol; |
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| 43 | double psi, gamma, beta; |
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| 44 | //form factors |
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| 45 | double sss, srr, srs; //cross |
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| 46 | double srr_1, srr_2, srr_3; |
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| 47 | double form_factor; |
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| 48 | tot_vol = num_strings * string_vol; |
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| 49 | tot_vol += num_pearls * pearl_vol; |
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| 50 | |
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| 51 | //sine functions of a pearl |
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| 52 | psi = sin(q_r); |
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| 53 | psi -= q_r * cos(q_r); |
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| 54 | psi *= 3.0; |
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| 55 | psi /= q_r * q_r * q_r; |
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| 56 | |
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| 57 | // Note take only 20 terms in Si series: 10 terms may be enough though. |
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| 58 | gamma = Si(q_edge); |
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| 59 | gamma /= (q_edge); |
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| 60 | beta = Si(q * (A_s - radius)); |
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| 61 | beta -= Si(q_r); |
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| 62 | beta /= q_edge; |
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| 63 | |
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| 64 | // form factor for num_pearls |
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| 65 | sss = 1.0 - pow(sincasq, num_pearls); |
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| 66 | sss /= oneminussinc * oneminussinc; |
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| 67 | sss *= -sincasq; |
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| 68 | sss -= num_pearls / 2.0; |
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| 69 | sss += num_pearls / oneminussinc; |
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| 70 | sss *= 2.0 * m_s * psi * m_s * psi; |
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| 71 | |
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| 72 | // form factor for num_strings (like thin rods) |
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| 73 | srr_1 = -sinc(q_edge/2.0) * sinc(q_edge/2.0); |
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| 74 | |
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| 75 | srr_1 += 2.0 * gamma; |
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| 76 | srr_1 *= num_strings; |
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| 77 | srr_2 = 2.0/oneminussinc; |
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| 78 | srr_2 *= num_strings; |
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| 79 | srr_2 *= beta * beta; |
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| 80 | srr_3 = 1.0 - pow(sincasq, num_strings); |
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| 81 | srr_3 /= oneminussinc * oneminussinc; |
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| 82 | srr_3 *= beta * beta; |
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| 83 | srr_3 *= -2.0; |
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| 84 | |
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| 85 | // total srr |
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| 86 | srr = srr_1 + srr_2 + srr_3; |
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| 87 | srr *= m_r * m_r; |
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| 88 | |
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| 89 | // form factor for correlations |
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| 90 | srs = 1.0; |
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| 91 | srs -= pow(sincasq, num_strings); |
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| 92 | srs /= oneminussinc * oneminussinc; |
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| 93 | srs *= -sincasq; |
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| 94 | srs += num_strings/oneminussinc; |
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| 95 | srs *= 4.0; |
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| 96 | srs *= (m_r * m_s * beta * psi); |
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| 97 | |
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| 98 | form_factor = sss + srr + srs; |
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| 99 | form_factor /= (tot_vol * 1.0e4); // norm by volume and A^-1 to cm^-1 |
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| 100 | |
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| 101 | return (form_factor); |
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| 102 | } |
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| 103 | |
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| 104 | double form_volume(double radius, double edge_sep, |
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| 105 | double thick_string, double num_pearls) |
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| 106 | { |
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| 107 | double total_vol; |
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| 108 | |
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| 109 | double number_of_strings = num_pearls - 1.0; |
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| 110 | |
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| 111 | double string_vol = edge_sep * M_PI * thick_string * thick_string / 4.0; |
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| 112 | double pearl_vol = M_4PI_3 * radius * radius * radius; |
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| 113 | |
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| 114 | total_vol = number_of_strings * string_vol; |
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| 115 | total_vol += num_pearls * pearl_vol; |
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| 116 | |
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| 117 | return(total_vol); |
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| 118 | } |
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| 119 | |
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| 120 | double Iq(double q, double radius, double edge_sep, |
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| 121 | double thick_string, double num_pearls, double sld, |
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| 122 | double string_sld, double solvent_sld) |
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| 123 | { |
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| 124 | double value, tot_vol; |
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| 125 | |
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| 126 | value = _pearl_necklace_kernel(q, radius, edge_sep, thick_string, |
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| 127 | num_pearls, sld, string_sld, solvent_sld); |
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| 128 | tot_vol = form_volume(radius, edge_sep, thick_string, num_pearls); |
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| 129 | |
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| 130 | return value*tot_vol; |
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| 131 | } |
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